First thing: 30 percent of the public don't know what ACA is, vs. only 12 percent when we asked about Obamacare. More on that later.

Now for the difference: 29 percent of the public supports Obamacare compared with 22 percent who support ACA. Forty-six percent oppose Obamacare and 37 percent oppose ACA. So putting Obama in the name raises the positives and the negatives. Gender and partisanship are responsible for the differences. Men, independents and Republicans are more negative on Obamacare than ACA. Young people, Democrats, nonwhites and women are more positive on Obamacare.

By way of context, a recent NBC/Wall Street Journal poll asked if respondents believe the new health care law is a good or bad idea. Their results: 31 percent think it's a good idea and 44 percent say bad idea—roughly in line with the Obamacare response. A quarter of respondents said they didn't know enough to have an opinion, equal to the share in the CNBC poll who don't know or are neutral on Obamacare.

The numbers about support for Obamacare vs. Affordable Care might seem at odds with the results CNBC released earlier this week showing Americans oppose defunding the new health care by a 44 percent to 38 percent margin and strongly opposed defunding it if it means shutting down the government.

Bill McInturff, a Republican pollster who conducts the survey for CNBC along with Democratic pollster Peter Hart, says Americans could be saying, whether they support it or not, "It's the law of the land. Let's give it a try."

Suggesting a huge uphill battle for the administration, feelings about the new health care are either negative or barely positive among those it seems most designed to help. For example, among people with incomes below $30,000, 19 percent don't know enough about Obamacare to have an opinion, and 31 percent have negative opinions compared with just 35 percent positive. Go up one income bracket to the $30,000 to $50,000 group and 51 percent have a negative view compared with 19 percent positive and 17 percent unsure.

One group that seems most informed on the issue: Republicans. While 30 percent of the public overall say they doesn't know enough about the Affordable Care Act to have an opinion, just 18 percent of Republicans and tea party supporters are unsure. Their opinions, of course, are highly negative.